During this event, there will be a different event expedition section. Completing expeditions will give various rewards, including Primogems, as well as hints to locate the new Geovishap enemies.
Each day, there are 8 different expedition locations. In each location, you can send out 4 of your characters to do the expedition. Certain characters have increased rate for getting a bonus, indicated by a small arrow going up on the bottom left of the character icons.
Additionally, you can also put it 1 extra character by using your friends' character that they have set. This is through the new system from the 1.3 update that lets players set a character in their profile. Be sure to utilize this to help out your friends with their expedition as well.
On the Hunt
As you progress with the expeditions, you will unlock "On the Hunt" challenges so that you can go against the new Geovishaps that's available in version 1.3.